A Bias-Corrected Bayesian Nonparametric Model for Combining Studies With Varying Quality in Meta-Analysis

Bayesian nonparametric (BNP) approaches for meta-analysis have been developed to relax distributional assumptions and handle the heterogeneity of random effects distributions. These models account for possible clustering and multimodality of the random effects distribution. However, when we combine studies of varying quality, the resulting posterior is not only a combination of the results of interest but also factors threatening the integrity of the studies' results. We refer to these factors as the studies' internal validity biases (e.g., reporting bias, data quality, and patient selection bias). In this paper, we introduce a new meta-analysis model called the bias-corrected Bayesian nonparametric (BC-BNP) model, which aims to automatically correct for internal validity bias in meta-analysis by only using the reported effects and their standard errors. The BC-BNP model is based on a mixture of a parametric random effects distribution, which represents the model of interest, and a BNP model for the bias component. This model relaxes the parametric assumptions of the bias distribution of the model introduced by Verde. Using simulated data sets, we evaluate the BC-BNP model and illustrate its applications with two real case studies. Our results show several potential advantages of the BC-BNP model: (1) It can detect bias when present while producing results similar to a simple normal-normal random effects model when bias is absent. (2) Relaxing the parametric assumptions of the bias component does not affect the model of interest and yields consistent results with the model of Verde. (3) In some applications, a BNP model of bias offers a better understanding of the studies' biases by clustering studies with similar biases. We implemented the BC-BNP model in the R package jarbes, facilitating its practical application.